Counting Up to Subtract - First Grade Mathematics

What do you do when you have to solve a subtraction problem like 9 - 7? If you try to count back 7 times, your fingers get tangled and you might lose count. But what if you could solve subtraction by counting forward? That brilliant strategy is called counting up to subtract! When the two numbers in a subtraction problem are close to each other, counting up from the smaller number to the bigger number reveals the difference in just a few quick hops. In this chapter, you will master the count-up strategy and see how addition and subtraction work hand in hand.

How the Count-Up Strategy Works

Instead of starting at the whole and moving backward, you start at the part you know and count forward until you reach the whole.

Solving 9 - 7 by Counting Up:

Step 1: Start at the smaller number (7):  "SEVEN..." (Tap your head!)
Step 2: Count forward until you reach 9:
        Hop 1: "Eight"  (Put up 1 finger)
        Hop 2: "Nine!"  (Put up 2 fingers - STOP! You reached 9!)

How many fingers are you holding up? 2 fingers!
Result: 9 - 7 = 2!

The Big Difference Between Counting Back and Counting Up:

When you count back, the last number you say with your mouth is the answer. When you count up, the number of fingers you are holding up is the answer! Your fingers track the distance between the two numbers.

Seeing Counting Up on the Number Path

Counting up measures the distance or gap between two points along the path.

Measuring the Gap from 7 to 9:
                        +1      +1
                      /-----\ /-----\
| 1| 2| 3| 4| 5| 6|[7]| 8 |[9]|10|
                    Start      Target (Stop!)

Distance traveled = 2 hops!
Therefore: 9 - 7 = 2

Why Counting Up Feels Natural

Counting up feels effortless because our brains naturally prefer counting forward (1, 2, 3...) rather than counting backward. Turning subtraction into a forward-counting game makes tricky problems feel easy.

Deciding Between Counting Back and Counting Up

Smart mathematicians examine the numbers before choosing their strategy.

The Strategy Decision Guide:
Problem: 10 - 2
Look at the numbers: 2 is small!
Strategy: COUNT BACK! ("10... 9, 8" -> Answer: 8)

Problem: 10 - 8
Look at the numbers: 8 is very close to 10!
Strategy: COUNT UP! ("8... 9, 10" -> 2 hops -> Answer: 2)

When to Count Up

Count up whenever the two numbers are close neighbors! If you are solving 8 - 6, 7 - 5, 9 - 8, or 10 - 7, the two numbers are near each other. Start at the smaller number and hop up to the larger number!

Practice Exercises

Exercise 1: Solve 8 - 6 using the count-up strategy. What number do you start with, what numbers do you say aloud, and how many hops do you take?

Exercise 2: Solve each of these problems by counting up: 7 - 5 = __ 10 - 8 = __ 6 - 4 = __ 9 - 8 = __

Exercise 3: For the problem 9 - 1, would you choose the count-back strategy or the count-up strategy? Explain your choice.

Exercise 4: A friend solves 8 - 7 by counting back 7 hops. Explain to your friend how counting up can solve this problem in just one hop.

Solutions and Explanations

Solution to Exercise 1: Start at the smaller number (6) and say: "Six..." Then count forward until you reach 8: "seven, eight." You took 2 hops (holding up 2 fingers), so 8 - 6 = 2.

Solution to Exercise 2: 7 - 5 = 2 (Start at 5: "6, 7" -> 2 hops) 10 - 8 = 2 (Start at 8: "9, 10" -> 2 hops) 6 - 4 = 2 (Start at 4: "5, 6" -> 2 hops) 9 - 8 = 1 (Start at 8: "9" -> 1 hop)

Solution to Exercise 3: For 9 - 1, choose the count-back strategy. Subtracting 1 requires only a single hop backward ("9... 8"), which takes less than a second.

Solution to Exercise 4: Tell your friend: "Since 7 and 8 are close neighbors, start at 7 and count up to 8! It only takes 1 hop ('7... 8'), so 8 - 7 = 1. That is much faster than counting backward 7 times!"